The cost of painting the total outside surface of a closed cylindrical oil tank as 50 paise per square decimatre is Rs. 198. The height of the tank is 6 times the radius of the base of the tank. Find the volume corredcted to 2 decimal places.
Answers
The volume of the cylindrical tank, correct to two decimal places, is 508.68 dm³.
• Let the radius of the base of the cylindrical tank be x dm.
According to the question,
Height of the tank = 6 × radius = 6x dm
• Given,
Cost of painting per dm² of the tank = 50 p
Cost of painting the total outside surface of the tank = Rs. 198 = 19800 p
• Total surface area of a closed cylinder (T.S.A.) = Curved surface area of the cylinder + Area of the base + Area of the top
∴ T.S.A. = 2πrh + πr² + πr²
Or, T.S.A. = 2πrh + 2πr²
Or, T.S.A. = 2πr (h + r)
where r is the radius, and h is the height of the cylinder.
• T.S.A. of the given cylindrical tank = 2π.x dm (6x dm + x dm)
= 2.(22/ 7).x dm.7x dm
= 2.22.x.x dm²
= 44x² dm²
• According to the question,
44x² × 50 p = 19800 p
Or, x² = 19800 p / (44 × 50p)
Or, x² = 9
Or, x = √9
Or, x = 3
• ∴ Radius of the base of the tank = 3 dm
Height of the tank = 6 × 3 dm = 18 dm
• Now, volume of the cylindrical tank = πr²h
Or, Volume of the tank = 3.14 × (3 dm)² × 18 dm
= 3.14 × 9 dm² × 18 dm
= 508.68 dm³
∴ Volume of the cylindrical tank, correct to two decimal places = 508.68 dm³